Sum-Free Sets Problem

✓ ShinkaEvolve Completed — 50 Generations

f(n) = max |S| where S ⊆ {1,...,n} and ∀a,b,c∈S: a + b ≠ c

Find the largest sum-free subset of {1, 2, ..., n}. A set is sum-free if no two elements sum to a third element in the set.

Best Score (n=100)

42.61

Generations

50

Set Size

~43

Compute

~2m

Cost

$16.29

Known Results

Theoretical Maximum: f(n) ≈ n/3 asymptotically (~33 for n=100)
Middle Third Construction: Take numbers in (n/3, 2n/3] — gives ~n/3 elements
Evolution Result: Set size of ~43 achieved (exceeds n/3!)
Finding: Initial middle-third construction was near-optimal; evolution confirmed

Full interactive visualization page coming soon...